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Estimation Of And Inference About The Expected Shortfall For Time Series With Infinite Variance

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  • Linton, Oliver
  • Xiao, Zhijie

Abstract

We study estimation and inference of the expected shortfall for time series with infinite variance. Both the smoothed and nonsmoothed estimators are investigated. The rate of convergence is determined by the tail thickness parameter, and the limiting distribution is in the stable class with parameters depending on the tail thickness parameter of the time series and on the dependence structure, which makes inference complicated. A subsampling procedure is proposed to carry out statistical inference. We also analyze a nonparametric estimator of the conditional expected shortfall. A Monte Carlo experiment is conducted to evaluate the finite sample performance of the proposed inference procedure, and an empirical application to emerging market exchange rates (from October 1997 to October 2008) is conducted to highlight the proposed study.

Suggested Citation

  • Linton, Oliver & Xiao, Zhijie, 2013. "Estimation Of And Inference About The Expected Shortfall For Time Series With Infinite Variance," Econometric Theory, Cambridge University Press, vol. 29(4), pages 771-807, August.
    • Handle: RePEc:cup:etheor:v:29:y:2013:i:04:p:771-807_00
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    Citations

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    Cited by:

    1. Oliver Linton & Yoon Jae Whang & Yu-Min Yen, 2021. "The lower regression function and testing expectation dependence dominance hypotheses," Econometric Reviews, Taylor & Francis Journals, vol. 40(8), pages 709-727, September.
    2. Gery Geenens & Richard Dunn, 2017. "A nonparametric copula approach to conditional Value-at-Risk," Papers 1712.05527, arXiv.org, revised Oct 2019.
    3. Tomasz Olma, 2021. "Nonparametric Estimation of Truncated Conditional Expectation Functions," Papers 2109.06150, arXiv.org.
    4. Steven Kou & Xianhua Peng, 2014. "On the Measurement of Economic Tail Risk," Papers 1401.4787, arXiv.org, revised Aug 2015.
    5. Le-Yu Chen & Yu-Min Yen, 2021. "Estimations of the Conditional Tail Average Treatment Effect," Papers 2109.08793, arXiv.org, revised Sep 2021.
    6. Chen, An & Nguyen, Thai & Stadje, Mitja, 2018. "Optimal investment under VaR-Regulation and Minimum Insurance," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 194-209.
    7. Daouia, Abdelaati & Stupfler, Gilles & Usseglio-Carleve, Antoine, 2022. "Inference for extremal regression with dependent heavy-tailed data," TSE Working Papers 22-1324, Toulouse School of Economics (TSE), revised 29 Aug 2023.
    8. Hill, Jonathan B. & Prokhorov, Artem, 2016. "GEL estimation for heavy-tailed GARCH models with robust empirical likelihood inference," Journal of Econometrics, Elsevier, vol. 190(1), pages 18-45.
    9. Geenens, Gery & Dunn, Richard, 2022. "A nonparametric copula approach to conditional Value-at-Risk," Econometrics and Statistics, Elsevier, vol. 21(C), pages 19-37.
    10. Juan Carlos Escanciano, 2020. "Uniform Rates for Kernel Estimators of Weakly Dependent Data," Papers 2005.09951, arXiv.org.
    11. Steven Kou & Xianhua Peng, 2016. "On the Measurement of Economic Tail Risk," Operations Research, INFORMS, vol. 64(5), pages 1056-1072, October.
    12. Trapani, Lorenzo, 2016. "Testing for (in)finite moments," Journal of Econometrics, Elsevier, vol. 191(1), pages 57-68.
    13. Xu, Ke-Li, 2020. "Inference of local regression in the presence of nuisance parameters," Journal of Econometrics, Elsevier, vol. 218(2), pages 532-560.

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